风花飘飘 发表于 2009-8-21 18:48:00

[求助] 黄金分割点的新问题——

qjchen 发表于 2009-8-23 09:32:00

<p>开始以为此图可以尺规完成，觉得可以用级数展开，后来想想连7边形都无法尺规，也就放弃了这个希望，google一下，得到如下资料。</p><p>1. 此角称为黄金角 </p><p>中文的wiki见此处</p><p><a href="http://zh.wikipedia.org/wiki/é&raquo;ƒé‡‘角">http://zh.wikipedia.org/wiki/%E9%BB%83%E9%87%91%E8%A7%92</a></p><p>英文的更详细的见此处</p><p><a href="http://zh.wikipedia.org/wiki/é&raquo;ƒé‡‘角">http://zh.wikipedia.org/wiki/%E9%BB%83%E9%87%91%E8%A7%92</a></p><p>而对于近似做法,springer出版社的期刊，给出了四种近似尺规做法</p><p><a href="http://www.springerlink.com/content/v518555826361k47/">http://www.springerlink.com/content/v518555826361k47/</a></p><p>pdf下载：<a href="http://www.springerlink.com/content/v518555826361k47/fulltext.pdf">http://www.springerlink.com/content/v518555826361k47/fulltext.pdf</a></p><p>示意图 </p><p></p><p>关于黄金角，查到的资料多少植物的，比如此处有一篇有趣的小文</p><p><a href="http://bbs.zomo.cn/thread-18478-1-1.html">http://bbs.zomo.cn/thread-18478-1-1.html</a></p><p></p>

风花飘飘 发表于 2009-8-25 13:38:00

<strong>時間長廊中的黃金分割比例<a href="http://cache.baidu.com/c?m=9d78d513d9c040aa4fece4690d61c0676953826639d3c4523f8a9c12d52219564615fea674734352849a273616af3e08b0a86c65377466eb8cc8ff1d8bfc852858ce6229314ddd164e824eb8cc32749c7cd60da8e904ecbded67d3fd8484c85327ca4e0e7dd4b1d0065503cd1bb1556bbee39a42085417eeac6b39aa4e705dde621aeb02faea25697387ebd65b1882718c340690db74f1644ff013a7081c5042b74bc50b462647ba0978&amp;p=8c7ac21f97904eab08e2922247&amp;user=baidu">http://cache.baidu.com/c?m=9d78d513d9c040aa4fece4690d61c0676953826639d3c4523f8a9c12d52219564615fea674734352849a273616af3e08b0a86c65377466eb8cc8ff1d8bfc852858ce6229314ddd164e824eb8cc32749c7cd60da8e904ecbded67d3fd8484c85327ca4e0e7dd4b1d0065503cd1bb1556bbee39a42085417eeac6b39aa4e705dde621aeb02faea25697387ebd65b1882718c340690db74f1644ff013a7081c5042b74bc50b462647ba0978&amp;p=8c7ac21f97904eab08e2922247&amp;user=baidu</a><p></p></strong>

xyp1964 发表于 2009-9-5 15:19:00

<p>黄金分割圆的迭代：</p><p></p><p></p><p>(defun c:tt ()<br/>&nbsp; (CMDLA0)<br/>&nbsp; (defun aaa (s1 / p1 leng l1 p2)<br/>&nbsp;&nbsp;&nbsp; (setq p1&nbsp;&nbsp; (xyp-get-CurveStartPoint s1)<br/>&nbsp;&nbsp; leng (xyp-get-CurveLength s1)<br/>&nbsp;&nbsp; l1&nbsp;&nbsp; (* leng (/ 2 (+ (sqrt 5) 1)))<br/>&nbsp;&nbsp; p2&nbsp;&nbsp; (XYP-GET-CURVEPOINTATDIST s1 (- leng l1))<br/>&nbsp;&nbsp;&nbsp; )<br/>&nbsp;&nbsp;&nbsp; (xyp-add-line p1 p2)<br/>&nbsp;&nbsp;&nbsp; (xyp-put "color" (entlast) 6)<br/>&nbsp;&nbsp;&nbsp; (distance p1 p2)<br/>&nbsp; )<br/>&nbsp; (setvar "osmode" 0)<br/>&nbsp; (xyp-MkLaCo "TEST" 1)<br/>&nbsp; (setq&nbsp;s1&nbsp; (car (entsel))<br/>&nbsp;p10 (xyp-get-dxf 10 s1)<br/>&nbsp;l&nbsp;&nbsp; (aaa s1)<br/>&nbsp;p0&nbsp; (xyp-get-CurveStartPoint s1)<br/>&nbsp;r1&nbsp; (xyp-get-dxf 40 s1)<br/>&nbsp; )<br/>&nbsp; (command "circle" "2p" p0 (polar p0 0 l))<br/>&nbsp; (setq&nbsp;s2&nbsp; (entlast)<br/>&nbsp;p20 (xyp-get-dxf 10 s2)<br/>&nbsp;r2&nbsp; (xyp-get-dxf 40 s2)<br/>&nbsp; )<br/>&nbsp; (repeat 100<br/>&nbsp;&nbsp;&nbsp; (setq r3 (* (aaa s2) 0.5))<br/>&nbsp;&nbsp;&nbsp; (command "circle" p10 (+ r1 r3))<br/>&nbsp;&nbsp;&nbsp; (setq s4 (entlast))<br/>&nbsp;&nbsp;&nbsp; (command "circle" p20 (+ r2 r3))<br/>&nbsp;&nbsp;&nbsp; (setq s5 (entlast))<br/>&nbsp;&nbsp;&nbsp; (command "circle" (cadr (xyp-get-Inters s4 s5 0)) r3)<br/>&nbsp;&nbsp;&nbsp; (setq s2&nbsp; (entlast)<br/>&nbsp;&nbsp; p20 (xyp-get-dxf 10 s2)<br/>&nbsp;&nbsp; r2&nbsp; (xyp-get-dxf 40 s2)<br/>&nbsp;&nbsp;&nbsp; )<br/>&nbsp;&nbsp;&nbsp; (entdel s4)<br/>&nbsp;&nbsp;&nbsp; (entdel s5)<br/>&nbsp; )<br/>&nbsp; (CMDLA1)<br/>)</p>

xyp1964 发表于 2009-9-5 15:37:00

填充效果：

qjchen 发表于 2009-9-5 17:22:00

<p>欢迎 xyp1964版主来指点 </p><p>这里也有不少未解的需要编程的计算几何题目，望院长解决 :)</p><p>BTW，我是xdcad的snoopychen</p>

wenwengg 发表于 2009-10-10 23:22:00

xyp1964发表于2009-9-5 15:19:00static/image/common/back.gif(defun c:tt ()&nbsp; (CMDLA0)...&nbsp; (CMDLA1))

<p>请问 (CMDLA0)&nbsp; (CMDLA1)是否自编函数<br/><br/></p>

redcat 发表于 2010-1-16 12:35:00

院长归来呀

秋忆CAD 发表于 2010-4-8 18:25:00

学习了

daidai9000 发表于 2010-5-11 10:39:00

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